Coupling of Finite-Element and Plane Waves Discontinuous Galerkin methods for time-harmonic problems

TL;DR

This paper introduces a coupling method combining finite element and plane waves discontinuous Galerkin techniques for efficient simulation of time-harmonic wave problems, maintaining optimal convergence rates.

Contribution

It presents a novel coupling strategy for finite element and wave-based methods applicable to Helmholtz problems, avoiding Lagrange multipliers and preserving convergence.

Findings

Coupling maintains the convergence rates of individual methods.

The approach reduces computational costs for high-frequency wave problems.

Validation confirms the method's effectiveness for complex geometries.

Abstract

A coupling approach is presented to combine a wave-based method to the standard finite element method. This coupling methodology is presented here for the Helmholtz equation but it can be applied to a wide range of wave propagation problems. While wave-based methods can significantly reduce the computational cost, especially at high frequencies, their efficiency is hindered by the need to use small elements to resolve complex geometric features. This can be alleviated by using a standard Finite-Element Model close to the surfaces to model geometric details and create large, simply-shaped areas to model with a wave-based method. This strategy is formulated and validated in this paper for the wave-based discontinuous Galerkin method together with the standard finite element method. The coupling is formulated without using Lagrange multipliers and results demonstrate that the coupling is optimal in that the convergence rates of the individual methods are maintained.